Question

рационал уравнения помогитеее

Answer 1

3)
$frac{x}{x+10} = frac{1}{x-8} \ \ frac{x}{x+10} - frac{1}{x-8} =0 \ \ frac{x(x-8)-(x+10)}{(x+10)(x-8)} =0 \ \ frac{x^2-8x-x-10}{(x+10)(x-8)} =0 \ \ frac{x^2-9x-10}{(x+10)(x-8)} =0 \ \ frac{(x-10)(x+1)}{(x+10)(x-8)} =0 \ \ left { {{(x-10)(x+1)=0} atop {(x+10)(x-8) neq 0}} right. \ \ 1) x-10 = 0; x_1=10 \ \ 2)x+1=0; x_2=-1$

4)
$frac{1}{3x-1} = frac{x}{27-x} \ \ frac{1}{3x-1} - frac{x}{27-x} =0 \ \ frac{27-x-x(3x-1)}{(3x-1)(27-x)}=0 \ \ frac{27-x-3x^2+x}{(3x-1)(27-x)}=0 \ \ frac{-3x^2+27}{(3x-1)(27-x)}=0 \ \ frac{3x^2-27}{(3x-1)(27-x)}=0 \ \ frac{3(x^2-9)}{(3x-1)(27-x)}=0 \ \ frac{3(x-3)(x+3)}{(3x-1)(27-x)}=0 \ \ left { {{3(x-3)(x+3)=0} atop {{(3x-1)(27-x) neq 0}} right. \ \1)x -3=0;x_1=3 \ 2)x+3=0;x_2=-3$